Course overview
This is an undergraduate course on single-variable calculus, aimed at
students in Faculty of Engineering. Following a rigorous, proof-based approach in
the spirit of Spivak, the course develops the mathematical foundations
of calculus, combining intuition and computation with precise
definitions and careful proofs.
Topics include: the real number system and completeness, functions,
limits and continuity, differentiation and its applications, convexity
and inequalities, Darboux and Riemann integration, the Fundamental
Theorem of Calculus, inverse functions, logarithmic, exponential and
trigonometric functions, integration techniques, improper integrals,
Taylor polynomials and remainder estimates, sequences and series,
power series, and uniform convergence.
Course page on Piazza:
piazza.com/cuhk.edu.hk/fall2026/estr1007
(enrolled students only) ·